Phase portraits of cubic polynomial Kolmogorov differential systems having a rational first integral of degree three [PDF]
Journal of Mathematical PhysicsWe classify all global phase portraits in the Poincaré disc of the cubic polynomial Kolmogorov differential systems having a well-defined rational first integral of degree three at the origin. For such differential systems there are exactly two different global phase portraits up to a reversal of the sense of their orbits.
Jaume Llibre, Renhao Tian
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Global centers of a class of cubic polynomial differential systems
Rendiconti del Circolo Matematico di Palermo Series 2A difficult classical problem in the qualitative theory of differential systems in the plane $\mathbb{R}^2$ is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center $p$ such that $\mathbb{R}^2\setminus\{p\}$
Jaume Llibre, Gabriel Rondón
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Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2 [PDF]
, 2016 Agraïments: FEDER-UNAB-10-4E-378, and a CAPES grant number 88881. 030454/2013-01 from the program CSF-PVE and CNPq grant "Projeto Universal 472796/2013-5".
de Moraes, Jaime R. +2 more
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On the cyclicity of Kolmogorov polycycles
Electronic Journal of Qualitative Theory of Differential Equations, 2022 In this paper we study planar polynomial Kolmogorov's differential systems \[ X_\mu\quad\begin{cases}{\dot{x}=f(x,y;\mu),}\\{\dot{y}=g(x,y;\mu),} \end{cases} \] with the parameter $\mu$ varying in an open subset $\Lambda\subset\mathbb{R}^N ...
David Marín, Jordi Villadelprat
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On a class of three-dimensional integrable Lagrangians [PDF]
, 2004 We characterize non-degenerate Lagrangians of the form $ \int f(u_x, u_y, u_t) dx dy dt $ such that the corresponding Euler-Lagrange equations $ (f_{u_x})_x+ (f_{u_y})_y+ (f_{u_t})_t=0 $ are integrable by the method of hydrodynamic reductions.
Ferapontov, E. V. +2 more
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Classical planar algebraic curves realizable by quadratic polynomial differential systems [PDF]
, 2017 In this paper we show planar quadratic polynomial differentialsystems exhibiting as solutions some famous planar invariant algebraic curves. Also we put particular attention to the Darboux integrability of these differential systems.The author is ...
García, I. A. (Isaac A.), Llibre, Jaume
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Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification [PDF]
, 2014 Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits.
Daniel, Luca +4 more
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Dynamics of a physically nonlinear viscoelastic cylindrical shell with a concentrated mass [PDF]
Инженерно-строительный журнал, 2019 It is known that the theory of linear and nonlinear elastic plates and shells is the most developed part of the theory of elasticity. In this area, the necessary equations are obtained and the methods to solve them are developed.
D.A. Khodzhaev +2 more
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On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems
Discrete Dynamics in Nature and Society, 2016 We study the number of limit cycles for the quadratic polynomial differential systems x˙=-y+x2, y˙=x+xy having an isochronous center with continuous and discontinuous cubic polynomial perturbations.
Ziguo Jiang
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A geometric approach to Catlin's boundary systems [PDF]
, 2018 For a point $p$ in a smooth real hypersurface $M\subset\C^n$, where the Levi form has the nontrivial kernel $K^{10}_p$, we introduce an invariant cubic tensor $\tau^3_p \colon \C T_p \times K^{10}_p \times \overline{K^{10}_p} \to \C\otimes (T_p/H_p ...
Zaitsev, Dmitri
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